Prove high-energy growth bound for gravitational amplitudes from first principles

Prove that the $2 \to 2$ amplitude of a consistent quantum gravity theory satisfies $M(s,t)/s^{2} \to 0\ \text{as}\ s \to \infty\ \text{at fixed}\ t < 0$ (so dispersion relations with two subtractions hold), using only unitarity, analyticity, crossing and polynomial or subexponential boundedness, in $D \ge 4$. Haring and Zhiboedov (2022) derived this bound with the extra assumption that scattering at large impact parameter is controlled by known semiclassical physics; justifying or removing that assumption, and handling $D = 4$ infrared divergences, is the open part.

A proof of the $s^{2}$ bound from axioms that do not assume semiclassical large-impact-parameter behavior, or a counterexample amplitude.